I assume the best would be to transfer all your information in your Google calendar so you can see it with your phone.Detailed instructions:

1. Select the "Personal" local calendar.Right-click and choose "Export calendar". The default format for the written file will be of the ".ics" format.

2. Import the data you just saved in your Google Calendar (the personal calendar). You may do it in either Google or Thunderbird.2a. Importing via Thunderbird– Under "Events and Tasks", select "Import"– Import the ".ics" file you created a few minutes ago (it may take a few minutes if you have lots of data)– Select the calendar into which you want to place the data.

3. Do the same for your "Work" calendar. If you want to keep your work calendar separate from your personal one, visit Google calendar and create a second calendar for your work data. Then export the work data from Thunderbird/Lightning and import it into the Work calendar you just created on Google.